The atmospheric pressure P in pounds per square inch (psi) is given by the formula below, where a is the altitude above sea level (in miles). If a city has an atmospheric pressure of 13.25 psi, what is its altitude? (Recall that 1 mi = 5,280 ft. Round your answer to the nearest foot.)
It would help to have the formula.
To find the altitude of the city, we need to rearrange the formula for atmospheric pressure in terms of altitude.
The given formula for atmospheric pressure P is not provided, so we cannot explicitly rearrange it in terms of altitude a. Without the formula, we can't determine the altitude of the city based solely on the given atmospheric pressure.
However, if we had the formula, we could rearrange it to solve for altitude a. The general formula relating atmospheric pressure P and altitude a is:
P = k * e^(-a/H)
Where:
P is the atmospheric pressure in psi,
a is the altitude above sea level in miles,
k is a constant,
e is the exponential function (approximately 2.71828),
and H is the scale height of the atmosphere.
Given the value of atmospheric pressure P as 13.25 psi, we could substitute this value into the formula and solve for altitude a.
Without the formula, it is not possible to determine the altitude of the city based solely on the given atmospheric pressure value.